Walking and running robots, in general, have significant ground to cover before they can approach the abilities of animals. Walking and running animals are able to attenuate significant disturbances, such as uneven ground, while maintaining excellent energy economy. Existing passive walkers, such as the Cornell Walker, are capable of energy economy similar to animals, but will fall in the presence of small disturbances. Robots that rely primarily on active control, such as Boston Dynamics' “BigDog,” can demonstrate impressive robustness to disturbances at the expense of energy economy. In contrast, humans and animals make excellent use of passive dynamics, but also use active control to compensate for disturbances. For example, guinea fowl are able to accommodate a drop in ground height by rapidly extending their leg into an unexpected disturbance, resulting in only slight deviation from their undisturbed gait. Furthermore, biomechanics studies suggest that humans and animals adjust muscle activation to accommodate changes in ground stiffness during hopping, walking, and running These types of active responses to ground disturbances are important on physical systems, where deviations from the undisturbed gait can lead to a loss of stability, falls, or springs exceeding their maximum deflection, potentially causing damage. Spring-mass models consisting of a mass bouncing on a spring provide a good approximation for animal running. However, while the simple spring-mass model is capable of some passive stability, without careful control of the leg angle at touchdown it tends to become unstable and fall.
A simple leg angle controller based on tuplets of natural frequency, zero-force leg length, apex hop height, and horizontal velocity may yield stable hopping gaits. Existing methods for selecting leg touchdown angles have included hand-tuned gain based controllers and constant leg retraction velocity control. (A. Seyfarth, H. Geyer, and H. Herr, “Swing-leg retraction: A simple control model for stable running,” The Journal of Experimental Biology, vol. 206, pp. 2547-2555, 2003.) However, these methods require tuning, and are subject to controller optimality.
A more reliable method of selecting a leg touchdown angle for SLIP model running, presented by Ernst et al., prevents falls by ensuring a center of mass trajectory during stance that is symmetrical about midstance. (M. Ernst, H. Geyer, and R. Blickhan, “Spring-legged locomotion on uneven ground: A control approach to keep the running speed constant,” in Proceedings of the 12th International Conference on Climbing and Walking Robots (CLAWAR), 2009). As used herein this type of gait will be referred to as an equilibrium gait, because every stride is the same as the last. In the interest of brevity, Ernst et al.'s method of selecting the leg touchdown angle will be referred to as the Ernst-Geyer-Blickhan (EGB) method. More recently, Hurst et al. have utilized active force control to improve legged locomotion as disclosed in U.S. Pat. No. 8,914,151.
It remains the case that when controlling a walking or running gait, one key challenge is the transition between swing (or flight) and stance for each leg and foot, also called a “Hybrid System.” The physics model of the system is different when the foot is in the air versus when it is on the ground. This presents challenges for the control and design of a machine. Thus, there remains a need in the art to create robots that better address the transition between swing (or flight) and stance, particularly for damped spring-mass legged machines.